Forex and Gambler’s Ruin

The concept of Gambler’s ruin refers a number of related statistical ideas, related to gambling and negative sum games. Typically the concept of Gambler’s ruin is used to persuade people that gambling against the house (for example in the casino) is likely to lead a gambler losing all of his bankroll. Others have attempted to apply these same statistical ideas, to retail Forex trading leading them to suggest that traders are likely to end losing all of their capital trading retail FX.

Gambler’s Ruin: It’s Application to Forex Trading

Gambler’s Ruin: Version Number 1

We shall start with the original application of the idea and how this same idea can be applied to FX trading. The original statistical idea is typically presented in the following way:

“A gambler who raises his bet to a fixed fraction of his bankroll when he wins, but doesn’t reduce it when he loses, will eventually lose his entire bankroll, even if his bets have a positive expected value.”

It should be clear how this particular idea can be applied to FX trading. A trader who wins his trades increases the number of Lots he trades each time he pulls of a successful trade. But the trader doesn’t scale back his trading volume after losing trades, meaning the size of his trades get increasingly large. Eventually, the trader will lose a trade which put’s his entire capital on the line at once. Clearly, this a case of bad money management, as no sensible trader would refuse to scale down his volume in-spite of losses.

Surprisingly, a number of trades do end up losing their capital, at least at a faster rate due to a similar phenomenon. Many traders begin trading a set volume and do not adjust this volume regardless of how well their account has been performing. This sees each trade putting a consistently larger percentage sum of their capital at risk, leading them into a situation where all of the capital is on the line. This version of the Gambler’s ruin, should not pose much a problem for those who are engaging in proper money management and have ensured they have adequate capital to begin with.

Gambler’s Ruin: Version Number 2

The second common application of the idea of Gambler’s ruin to Forex, goes as follows;

“Two gamblers, begin flipping a coin with one another betting a $1 on each flip. The coin is fair meaning that each player is equally as likely to win each bet. However, one player starts with a $100 bankroll, while the other player begins with an infinite or significant sum such as $100,000. Despite each player having an equal chance of winning each individual bet, the player with the smaller bankroll is extremely likely to go bust first. Though, this will likely take a huge number of coin flips to happen.”

Again, it should be quite easy to see how this can be applied to Forex, particularly to retail FX traders who tend to have limited amount of capital in the first place. Imagine, you are trading against a market maker/dealing desk broker, and each time you place a trade you either win or lose.

With possible two results we are going to assume a trader has an about 50% chance of winning a trade. However, the broker is much better capitalised than the trader, so the broker can simply wait out a traders winning streak, until things turn against the trader. Ultimately, leading to the trader lose all of his capital to the market maker. This is one way, which market makers are able to profit without any form of manipulation or hedging. In fact, the situation is worse for the retail trader who has to pay the broker a spread each time he enters into the market, meaning that things are skewed slightly into the brokers favour.

The form of Gambler’s ruin can also be applied to traders who are trading with Non-Dealing Desk/STP Brokers. In this application, the opposing player is not the brokerage but rather all the opposing and liquidity providers active in the FX market. Retail Traders are by definition less capitalised than professional and institutional traders. This in essence means that the institutional players are able to bare longer losing streaks, while a short losing streak has the potential to wipe out a retail trader. By simply, remaining an active market participant in theory the institutional or professional trader can profit from those who are less capitalised.

This application of gamblers ruin to retail FX trading is particularly contentious, as it assumes that FX is a fair game. This would see the result of each trade being equivalent to the flip of a coin. Most skilled traders would object that FX trading involves a considerable amount of skill, and the best traders can call the market with a high degree of accuracy/profitability. What this application does highlight is the benefits that being highly capitalised has on potential account performance, as it allows traders/institutions to remain in the market and profit when they experience big moves in their favour.

Gambler’s Ruin: Verison Number 3

This is the most common use of the idea today, and goes as follows:

“A gambler playing a negative sum game, will eventually go broke regardless of his betting system.”

Someone who plays Roulette will eventually go bust, if he continues to play indefinitely due to the fact that the odds are set with a built in advantage given to the house. Now some people claim that Forex is a Negative Sum game, as all profits are made at the expensive of other traders and that brokers collect spreads taking money out of the ‘prize pool’. For one it is highly contentious whether Spot Forex is even a Zero Sum game, for a summary of the controversy we recommend you read this article.

Spot FX, could even be a negative sum game but akin to Poker played in a casino. Poker is a widely accepted Zero Sum game, as one player can only profit at the expense of another player. When played casinos, the casino takes a share of each pot known as ‘the rake’. This turns casino Poker into a negative sum game. It should be noted that there are many Poker players, who consistently turn a profit playing Poker in a casino, despite it being a negative sum game. There is no reason why the same could not be true for Spot FX traders, even if one accepted that trading Spot FX was a negative sum game (which is controversial in itself).

Gambler’s Ruin and Forex: Conclusions

While the idea of Gambler’s ruin can be applied to retail FX trading, none of the applications are perfect. But each of the various application of the general idea of gambler’s ruin, does help highlight some of the challenges faced by traders. It also helps explain why the vast majority of retail FX traders lose money.